The collective nouns of English came about in an almost artistic fashion. What I mean is that historically hunters came up with these mass nouns as "terms of venery". The collective part normally does not have any direct etymological link to the word 'group' or its synonyms, but functions the same as other grammatical terms to denote mass nouns.
I highly recommend a read through of James Lipton's An Exaltation of Larks, which gives some brief history of mass nouns in English, and dedicates the majority of the book to lists of various terms. Also see Collective Noun for a good description of their use.